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On the Implications of the Log-normal Path Loss Model:
An Efficient Method to Deploy and Move Sensor Motes
Yin Chen, Andreas Terzis
November 2, 2011
• What to do about the transitional region?– Place motes in the transitional region vs in the connected
region
Transitional region
2
Connected region
Our Proposal
• Occupy the transitional region– Perform random trials to construct links with high PRR– Based on the Log-normal radio model
3
Outline
• Introduce log-normal path loss model
• Discuss pitfalls
• Present the experimental results – reality check
5
Log-normal Path Loss Model
• Received signal strength at a distance is
– , is a Gaussian random variable• Due to artifacts in the environment (occlusions, multipath, etc.)
– Does not consider temporal variation
Power of the transmitted signal
Path loss at distance
Path loss exponent
Random variation
Sender Receiverdistance
6
Three Regions of Radio Links
• As the distance increases, we go through 3
regions– Connected:– Transitional: – Disconnected:
• Observation– The packet reception ratio at any given location is random 7
Connected Region
• In connected region
• PRR is very likely to be
high
• Trying one location will
likely produce good link
Sender Receiver5 meters
8
Transitional Region
• In transitional region
• PRR may or may not be
high
• Trying a few spots should
yield a good link
Sender Receiver15 meters
9
Disconnected Region
• In disconnected region
• PRR is very unlikely to be
high
• Trying multiple spots
seems worthless
Sender Receiver40 meters
10
Outline
• Introduce log-normal path loss model
• Discuss pitfalls
• Present the experimental results – reality check
11
Pitfalls
• Log-normal path loss model is not perfect
• The Gaussian variation in signal strength is a
statistical observation
• Signal strengths at nearby locations are
correlated
12
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
13
Experimental Setup
• Devices– TelosB motes– iRobot with an Ebox-3854 running Linux
• Environments– Outdoor parking lot– Lawn– Indoor hallway– Indoor testbed– Two forests
14
Evaluations on the Log-normal Model
• Holds well in all the environments– Example figure for the parking lot
– We can subtract the solid line from the raw RSSI readings• The residual RSSI values are samples of the random variable :
15
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
17
Spatial Correlation
• PRR measurements at a parking lot– iRobot moves in a 2-d plane (the ground)– Black cell : PRR below 85%; Gray cell : PRR above 85%
• PRR are correlated• Trying two adjacent locations
flipping two coins
• In all of our experiments, 1 meter is sufficient to remove most correlation
18
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
19
Number of Trials - Configuration
• Grid sampling– Bernoulli trials
• Number of trials to find a good PRR is
geometrically distributed
distance
1 meter
20
Number of Trials - Results• Measure and compute the length of connected region
– Place motes at distances longer than
Parking Lot
Hallway 1 Hallway 2 Office Forest0
0.5
1
1.5
2
2.5
3
3.5
Number of Trials Expected Number of Trials
Park
ing
Lot
Hallw
ay 1
Hallw
ay 2
Office
Fore
st0
0.5
1
1.5
2
2.5
3
3.5
Distance to the Sender (Normalized by lc)
21
Number of Trials – Fitting Geometric Distribution
Suggests that 1 meter
ensures independent
trials.
22
Connecting Two Motes
Mote A Mote BRelay
TAR: number of trials to connect to A
TBR: number of trials to connect to B
TARB: number of trials to connect to both A and B
Hallway 1 Hallway 2 Parking Lot 1
Parking Lot 2
Parking Lot 3
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
TAR TBRTARB TAR multiplied by TBR
23
TARB TAR TBR
Reality Check
• Verify log-normal path loss model
• Quantify spatial correlations
• Count number of trials to construct good links
• Investigate temporal variations
24
Conclusion
• Log-normal model fits sensornets
• Signal correlation vanishes at 1 meter separation
• Easy to find good links in the transitional region– Rule of thumb: at twice the length of connected region,
number of trials is less than 5 with high probability
26
Application – Placing Relay Nodes
• Number of relay nodes at large scale– Place 120 sensor motes in an area of size 800m by 800m – Run Steiner Tree algorithm to place relay nodes
27
Application – Mobile Sensor Networks
• Mobile sink– If the current spot yields low PRR, move 1 meter– Minimize travel distance
• Mobile motes
Signal variation in the space domain
Signal variation in the time domain
28
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